The Role of the Tumor Microenvironment in Glioblastoma: A Mathematical Model

The antitumor action of endocannabinoids in the tumor microenvironment of glioblastoma

Approximately 80% of all malignant brain tumors are gliomas, which are primary brain tumors. The most prevalent subtype of glioma, glioblastoma multiforme (GBM), is also the most deadly. Chemotherapy, immunotherapy, surgery, and conventional pharmacotherapy are currently available therapeutic options for GBM; unfortunately, these approaches only prolong the patient's life by 5 years at most. Despite numerous intensive therapeutic options, GBM is considered incurable. Accumulating preclinical data indicate that overt antitumoral effects can be induced by pharmacologically activating endocannabinoid receptors on glioma cells by modifying important intracellular signaling cascades. The complex mechanism underlying the endocannabinoid receptor-evoked antitumoral activity in experimental models of glioma may inhibit the ability of cancer cells to invade, proliferate, and exhibit stem cell-like characteristics, along with altering other aspects of the complex tumor microenvironment. The exact biological function of the endocannabinoid system in the development and spread of gliomas, however, is remains unclear and appears to rely heavily on context. Previous studies have revealed that endocannabinoid receptors are present in the tumor microenvironment, suggesting that these receptors could be novel targets for the treatment of GBM. Additionally, endocannabinoids have demonstrated anticancer effects through signaling pathways linked to the classic features of cancer. Thus, the pharmacology of endocannabinoids in the glioblastoma microenvironment is the main topic of this review, which may promote the development of future GBM therapies.

Macrophage's role in solid tumors: two edges of a sword

The tumor microenvironment is overwhelmingly dictated by macrophages, intimately affiliated with tumors, exercising pivotal roles in multiple processes, including angiogenesis, extracellular matrix reconfiguration, cellular proliferation, metastasis, and immunosuppression. They further exhibit resilience to chemotherapy and immunotherapy via meticulous checkpoint blockades. When appropriately stimulated, macrophages can morph into a potent bidirectional component of the immune system, engulfing malignant cells and annihilating them with cytotoxic substances, thus rendering them intriguing candidates for therapeutic targets. As myelomonocytic cells relentlessly amass within tumor tissues, macrophages rise as prime contenders for cell therapy upon the development of chimeric antigen receptor effector cells. Given the significant incidence of macrophage infiltration correlated with an unfavorable prognosis and heightened resistance to chemotherapy in solid tumors, we delve into the intricate role of macrophages in cancer propagation and their promising potential in confronting four formidable cancer variants-namely, melanoma, colon, glioma, and breast cancers.

Immune-checkpoint inhibitor therapy response evaluation using oncophysics-based mathematical models

The field of oncology has transformed with the advent of immunotherapies. The standard of care for multiple cancers now includes novel drugs that target key checkpoints that function to modulate immune responses, enabling the patient's immune system to elicit an effective anti-tumor response. While these immune-based approaches can have dramatic effects in terms of significantly reducing tumor burden and prolonging survival for patients, the therapeutic approach remains active only in a minority of patients and is often not durable. Multiple biological investigations have identified key markers that predict response to the most common form of immunotherapy-immune checkpoint inhibitors (ICI). These biomarkers help enrich patients for ICI but are not 100% predictive. Understanding the complex interactions of these biomarkers with other pathways and factors that lead to ICI resistance remains a major goal. Principles of oncophysics-the idea that cancer can be described as a multiscale physical aberration-have shown promise in recent years in terms of capturing the essence of the complexities of ICI interactions. Here, we review the biological knowledge of mechanisms of ICI action and how these are incorporated into modern oncophysics-based mathematical models. Building on the success of oncophysics-based mathematical models may help to discover new, rational methods to engineer immunotherapy for patients in the future. This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

SPTSSA Is a Prognostic Marker for Glioblastoma Associated with Tumor-Infiltrating Immune Cells and Oxidative Stress

Background. SPTSSA encodes the small subunit A of serine palmitoyltransferase. It catalyzes the formation of sphingoid long-chain base backbone of sphingolipids. Its role in glioma prognosis and tumor-infiltrating immune cells remains unclear. Methods. We analyzed SPTSSA expression and association with clinical prognosis using GEPIA and CGGA database. Then, GSEA was performed to identify relevant biological functions of SPTSSA. The correlations between SPTSSA expression and tumor immune infiltrates were investigated using CIBERSORT and TIMER. Finally, IHC and IF were performed to confirm the value of prognosis and the correlation with immune infiltration. Results. SPTSSA expression was significantly upregulated in diffuse glioma compared to normal tissues and associated with poor survival in GEPIA and CGGA database. Then, we identified biological processes and signaling pathways associated with SPTSSA expression. The result showed that SPTSSA enriched in the GO term like oxidative stress. Finally, we showed that SPTSSA expression was significantly associated with tumor-infiltrating immune cells and overall survival via IHC. Conclusion. These findings suggest that SPTSSA expression might be used as a prognostic biomarker for glioma and potential target for novel glioma therapy.

Tumor Microenvironment in Glioma Invasion

A major malignant trait of gliomas is their remarkable infiltration capacity. When glioma develops, the tumor cells have already reached the distant part. Therefore, complete removal of the glioma is impossible. Recently, research on the involvement of the tumor microenvironment in glioma invasion has advanced. Local hypoxia triggers cell migration as an environmental factor. The transcription factor hypoxia-inducible factor (HIF) -1α, produced in tumor cells under hypoxia, promotes the transcription of various invasion related molecules. The extracellular matrix surrounding tumors is degraded by proteases secreted by tumor cells and simultaneously replaced by an extracellular matrix that promotes infiltration. Astrocytes and microglia become tumor-associated astrocytes and glioma-associated macrophages/microglia, respectively, in relation to tumor cells. These cells also promote glioma invasion. Interactions between glioma cells actively promote infiltration of each other. Surgery, chemotherapy, and radiation therapy transform the microenvironment, allowing glioma cells to invade. These findings indicate that the tumor microenvironment may be a target for glioma invasion. On the other hand, because the living body actively promotes tumor infiltration in response to the tumor, it is necessary to reconsider whether the invasion itself is friend or foe to the brain.

Glioblastoma Microenvironment and Cellular Interactions

Simple Summary

This paper summarizes the crosstalk between tumor/non-tumor cells and other elements of the glioblastoma (GB) microenvironment. In tumor pathology, glial cells result in the highest number of cancers, and GB is considered the most lethal tumor of the central nervous system (CNS). The tumor microenvironment (TME) is a complex peritumoral hallo composed of tumor cells and several non-tumor cells (e.g., nervous cells, stem cells, fibroblasts, vascular and immune cells), which might be a key factor for the ineffective treatment since the microenvironment modulates the biologic status of the tumor with the increase in its evasion capacity. A deeper understanding of cell–cell interactions in the TME and with the tumor cells could be the basis for a more efficient therapy.

Abstract

The central nervous system (CNS) represents a complex network of different cells, such as neurons, glial cells, and blood vessels. In tumor pathology, glial cells result in the highest number of cancers, and glioblastoma (GB) is considered the most lethal tumor in this region. The development of GB leads to the infiltration of healthy tissue through the interaction between all the elements of the brain network. This results in a GB microenvironment, a complex peritumoral hallo composed of tumor cells and several non-tumor cells (e.g., nervous cells, stem cells, fibroblasts, vascular and immune cells), which might be the principal factor for the ineffective treatment due to the fact that the microenvironment modulates the biologic status of the tumor with the increase in its evasion capacity. Crosstalk between glioma cells and the brain microenvironment finally inhibits the beneficial action of molecular pathways, favoring the development and invasion of the tumor and its increasing resistance to treatment. A deeper understanding of cell–cell interactions in the tumor microenvironment (TME) and with the tumor cells could be the basis for a more efficient therapy.

Optimal regulation of tumour-associated neutrophils in cancer progression

In a tumour microenvironment, tumour-associated neutrophils could display two opposing differential phenotypes: anti-tumour (N1) and pro-tumour (N2) effector cells. Converting N2 to N1 neutrophils provides innovative therapies for cancer treatment. In this study, a mathematical model for N1-N2 dynamics describing the cancer survival and immune inhibition in response to TGF-β and IFN-β is considered. The effects of exogenous intervention of TGF-β inhibitor and IFN-β are examined in order to enhance N1 recruitment to combat tumour progression. Our approach employs optimal control theory to determine drug infusion protocols that could minimize tumour volume with least administration cost possible. Four optimal control scenarios corresponding to different therapeutic strategies are explored, namely, TGF-β inhibitor control only, IFN-β control only, concomitant TGF-β inhibitor and IFN-β controls, and alternating TGF-β inhibitor and IFN-β controls. For each scheme, different initial conditions are varied to depict different pathophysiological condition of a cancer patient, leading to adaptive treatment schedule. TGF-β inhibitor and IFN-β drug dosages, total drug amount, infusion times and relative cost of drug administrations are obtained under various circumstances. The control strategies achieved could guide in designing individualized therapeutic protocols.

Atorvastatin-mediated rescue of cancer-related cognitive changes in combined anticancer therapies

Acute administration of trastuzumab (TZB) may induce various forms of cognitive impairment. These cancer-related cognitive changes (CRCC) are regulated by an adverse biological process involving cancer stem cells (CSCs) and IL-6. Recent studies have reported that atorvastatin (ATV) may change the dynamic of cognitive impairment in a combination (TZB+ATV) therapy. In this study, we investigate the mutual interactions between cancer stem cells and the tumor cells that facilitate cognitive impairment during long term TZB therapy by developing a mathematical model that involves IL-6 and the key apoptotic regulation. These include the densities of tumor cells and CSCs, and the concentrations of intracellular signaling molecules (NFκB, Bcl-2, BAX). We apply the mathematical model to a single or combination (ATV+TZB) therapy used in the experiments to demonstrate that the CSCs can enhance CRCC by secreting IL-6 and ATV may interfere the whole regulation. We show that the model can both reproduce the major experimental observation on onset and prevention of CRCC, and suggest several important predictions to guide future experiments with the goal of the development of new anti-tumor and anti-CRCC strategies. Moreover, using this model, we investigate the fundamental mechanism of onset of cognitive impairment in TZB-treated patients and the impact of alternating therapies on the anti-tumor efficacy and intracellular response to different treatment schedules.

A conventional drug, trastuzumab (TZB), was shown to be an effective weapon in killing cancer cells in brain. However, long term treatment of TZB increases the proportion of cancer stem cells (CSCs) in the tumour microenvironment (TME) and induces up-regulation of pro-tumoral molecules such as IL-6 in TME. These cancer cells then become more resistant to this chemotherapy through the IL-mediated up-regulation of NFκB and CSCs. More importantly, these changes in TME result in a serious side effect, cognitive impairment called cancer-related cognitive changes (CRCC). The detailed mechanism of CRCC is still poorly understood. However, cancer patients with chemotherapy-induced cognitive impairment can have long-term or delayed mental changes. In this study, we investigated the fundamental mechanism of CRCC in cancer patients based on experiments and a mathematical model that describes how tumor cells interact with CSCs in response to chemo drugs. In particular, we investigate how TZB-induced CSCs with modified IL-6 landscapes shape the cognitive functions in cancer patients. We showed that the combination treatment with another drug, atorvastatin (ATV), can abrogate the TZB-induced CRCC and enhance the survival probability of cancer patients by synergistic anti-tumor effect. We demonstrate that the cognitive functions and survival rates in cancer patients depend on the apoptotic signaling pathways via the critical communication and IL-6 landscapes of stimulated CTCs.

Mathematical model of STAT signalling pathways in cancer development and optimal control approaches

In various diseases, the STAT family display various cellular controls over various challenges faced by the immune system and cell death programs. In this study, we investigate how an intracellular signalling network (STAT1, STAT3, Bcl-2 and BAX) regulates important cellular states, either anti-apoptosis or apoptosis of cancer cells. We adapt a mathematical framework to illustrate how the signalling network can generate a bi-stability condition so that it will induce either apoptosis or anti-apoptosis status of tumour cells. Then, we use this model to develop several anti-tumour strategies including IFN-β infusion. The roles of JAK-STATs signalling in regulation of the cell death program in cancer cells and tumour growth are poorly understood. The mathematical model unveils the structure and functions of the intracellular signalling and cellular outcomes of the anti-tumour drugs in the presence of IFN-β and JAK stimuli. We identify the best injection order of IFN-β and DDP among many possible combinations, which may suggest better infusion strategies of multiple anti-cancer agents at clinics. We finally use an optimal control theory in order to maximize anti-tumour efficacy and minimize administrative costs. In particular, we minimize tumour volume and maximize the apoptotic potential by minimizing the Bcl-2 concentration and maximizing the BAX level while minimizing total injection amount of both IFN-β and JAK2 inhibitors (DDP).

An in silico glioblastoma microenvironment model dissects the immunological mechanisms of resistance to PD-1 checkpoint blockade immunotherapy

The PD-1 immune checkpoint-based therapy has emerged as a promising therapy strategy for treating the malignant brain tumor glioblastoma (GBM). However, patient response varies in clinical trials due in large to the tumor heterogeneity and immunological resistance in the tumor microenvironment. To further understand how mechanistically the niche interplay and competition drive anti-PD-1 resistance, we established an in-silico model to quantitatively describe the biological rationale of critical GBM-immune interactions, such as tumor growth and apoptosis, T cell activation and cytotoxicity, and tumor-associated macrophage (TAM) mediated immunosuppression. Such an in-silico experimentation and predictive model, based on the in vitro microfluidic chip-measured end-point data and patient-specific immunological characteristics, allowed for a comprehensive and dynamic analysis of multiple TAM-associated immunosuppression mechanisms against the anti-PD-1 immunotherapy. Our computational model demonstrated that the TAM-associated immunosuppression varied in severity across different GBM subtypes, which resulted in distinct tumor responses. Our prediction results indicated that a combination therapy co-targeting of PD-1 checkpoint and TAM-associated CSF-1R signaling could enhance the immune responses of GBM patients, especially those patients with mesenchymal GBM who are irresponsive to the single anti-PD-1 therapy. The development of a patient-specific in silico-in vitro GBM model would help navigate and personalize immunotherapies for GBM patients.

Macrophages/Microglia in the Glioblastoma Tumor Microenvironment

The complex interaction between glioblastoma and its microenvironment has been recognized for decades. Among various immune profiles, the major population is tumor-associated macrophage, with microglia as its localized homolog. The present definition of such myeloid cells is based on a series of cell markers. These good sentinel cells experience significant changes, facilitating glioblastoma development and protecting it from therapeutic treatments. Huge, complicated mechanisms are involved during the overall processes. A lot of effort has been dedicated to crack the mysterious codes in macrophage/microglia recruiting, activating, reprogramming, and functioning. We have made our path. With more and more key factors identified, a lot of new therapeutic methods could be explored to break the ominous loop, to enhance tumor sensitivity to treatments, and to improve the prognosis of glioblastoma patients. However, it might be a synergistic system rather than a series of clear, stepwise events. There are still significant challenges before the light of truth can shine onto the field. Here, we summarize recent advances in this field, reviewing the path we have been on and where we are now.

Multiscale phenomena and patterns in biological systems: special issue in honour of Hans Othmer

This special issue on "Multiscale phenomena and patterns in biological systems" is an homage to the seminal contributions of Hans Othmer. He has remained at the forefront of multiscale modelling and pattern formation in biology for over half a century, developing models for molecular signalling networks, the mechanics of cellular movements, the interactions between multiple cells and their contributions to tissue patterning and dynamics. The contributions in this special issue follow Hans' legacy in using advanced mathematics to understand complex biological processes.

Role of neutrophil extracellular traps in regulation of lung cancer invasion and metastasis: Structural insights from a computational model

Lung cancer is one of the leading causes of cancer-related deaths worldwide and is characterized by hijacking immune system for active growth and aggressive metastasis. Neutrophils, which in their original form should establish immune activities to the tumor as a first line of defense, are undermined by tumor cells to promote tumor invasion in several ways. In this study, we investigate the mutual interactions between the tumor cells and the neutrophils that facilitate tumor invasion by developing a mathematical model that involves taxis-reaction-diffusion equations for the critical components in the interaction. These include the densities of tumor and neutrophils, and the concentrations of signaling molecules and structure such as neutrophil extracellular traps (NETs). We apply the mathematical model to a Boyden invasion assay used in the experiments to demonstrate that the tumor-associated neutrophils can enhance tumor cell invasion by secreting the neutrophil elastase. We show that the model can both reproduce the major experimental observation on NET-mediated cancer invasion and make several important predictions to guide future experiments with the goal of the development of new anti-tumor strategies. Moreover, using this model, we investigate the fundamental mechanism of NET-mediated invasion of cancer cells and the impact of internal and external heterogeneity on the migration patterning of tumour cells and their response to different treatment schedules.

Modeling invasion patterns in the glioblastoma battlefield

Glioblastoma is the most aggressive tumor of the central nervous system, due to its great infiltration capacity. Understanding the mechanisms that regulate the Glioblastoma invasion front is a major challenge with preeminent potential clinical relevances. In the infiltration front, the key features of tumor dynamics relate to biochemical and biomechanical aspects, which result in the extension of cellular protrusions known as tumor microtubes. The coordination of metalloproteases expression, extracellular matrix degradation, and integrin activity emerges as a leading mechanism that facilitates Glioblastoma expansion and infiltration in uncontaminated brain regions. We propose a novel multidisciplinary approach, based on in vivo experiments in Drosophila and mathematical models, that describes the dynamics of active and inactive integrins in relation to matrix metalloprotease concentration and tumor density at the Glioblastoma invasion front. The mathematical model is based on a non-linear system of evolution equations in which the mechanisms leading chemotaxis, haptotaxis, and front dynamics compete with the movement induced by the saturated flux in porous media. This approach is able to capture the relative influences of the involved agents and reproduce the formation of patterns, which drive tumor front evolution. These patterns have the value of providing biomarker information that is related to the direction of the dynamical evolution of the front and based on static measures of proteins in several tumor samples. Furthermore, we consider in our model biomechanical elements, like the tissue porosity, as indicators of the healthy tissue resistance to tumor progression.

Glioblastoma (GB) is a type of brain cancer that originated from glial cells. The infiltrative nature of GB cells is a key feature for understanding its aggressiveness and resistance to current treatments. Cellular protrusions, named as Tumor Microtubes (TMs) in GB, mediate the interaction between tumor and healthy tissue and the processes leading GB invasion. These protrusions are also responsible for several cell communication pathways (e.g. Hedgehog or WNT). We have developed a multidisciplinary approach, which combined biological biomarker measurements performed in Drosophila GB with a novel mathematical model, to determine the interactions between proteases, integrins, and TM dynamics. The resulting model is able to predict the formation and infiltration of GB fronts, and, therefore, the directionality, aggressiveness, and progression of the tumor.

Analysis of the Parametric Correlation in Mathematical Modeling of In Vitro Glioblastoma Evolution Using Copulas

Modeling and simulation are essential tools for better understanding complex biological processes, such as cancer evolution. However, the resulting mathematical models are often highly non-linear and include many parameters, which, in many cases, are difficult to estimate and present strong correlations. Therefore, a proper parametric analysis is mandatory. Following a previous work in which we modeled the in vitro evolution of Glioblastoma Multiforme (GBM) under hypoxic conditions, we analyze and solve here the problem found of parametric correlation. With this aim, we develop a methodology based on copulas to approximate the multidimensional probability density function of the correlated parameters. Once the model is defined, we analyze the experimental setting to optimize the utility of each configuration in terms of gathered information. We prove that experimental configurations with oxygen gradient and high cell concentration have the highest utility when we want to separate correlated effects in our experimental design. We demonstrate that copulas are an adequate tool to analyze highly-correlated multiparametric mathematical models such as those appearing in Biology, with the added value of providing key information for the optimal design of experiments, reducing time and cost in in vivo and in vitro experimental campaigns, like those required in microfluidic models of GBM evolution.

Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution

In silico models and computer simulation are invaluable tools to better understand complex biological processes such as cancer evolution. However, the complexity of the biological environment, with many cell mechanisms in response to changing physical and chemical external stimuli, makes the associated mathematical models highly non-linear and multiparametric. One of the main problems of these models is the determination of the parameters’ values, which are usually fitted for specific conditions, making the conclusions drawn difficult to generalise. We analyse here an important biological problem: the evolution of hypoxia-driven migratory structures in Glioblastoma Multiforme (GBM), the most aggressive and lethal primary brain tumour. We establish a mathematical model considering the interaction of the tumour cells with oxygen concentration in what is called the go or grow paradigm. We reproduce in this work three different experiments, showing the main GBM structures (pseudopalisade and necrotic core formation), only changing the initial and boundary conditions. We prove that it is possible to obtain versatile mathematical tools which, together with a sound parametric analysis, allow to explain complex biological phenomena. We show the utility of this hybrid “biomimetic in vitro-in silico” platform to help to elucidate the mechanisms involved in cancer processes, to better understand the role of the different phenomena, to test new scientific hypotheses and to design new data-driven experiments.

Collective invasion of glioma cells through OCT1 signalling and interaction with reactive astrocytes after surgery

Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and cellular infiltration of normal brain tissue. miR-451 and its downstream molecules are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in the tumour microenvironment (TME). Surgery-induced transition in reactive astrocyte populations can play a significant role in tumour dynamics. In this work, we develop a multi-scale mathematical model of miR-451-LKB1-AMPK-OCT1-mTOR pathway signalling and individual cell dynamics of the tumour and reactive astrocytes after surgery. We show how the effects of fluctuating glucose on tumour cells need to be reprogrammed by taking into account the recent history of glucose variations and an AMPK/miR-451 reciprocal feedback loop. The model shows how variations in glucose availability significantly affect the activity of signalling molecules and, in turn, lead to critical cell migration. The model also predicts that microsurgery of a primary tumour induces phenotypical changes in reactive astrocytes and stem cell-like astrocytes promoting tumour cell proliferation and migration by Cxcl5. Finally, we investigated a new anti-tumour strategy by Cxcl5-targeting drugs. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Patient-Derived Glioma Models: From Patients to Dish to Animals

Glioblastoma (GBM) is the most common and malignant primary brain tumor in adults associated with a poor survival. Current standard of care consists of surgical resection followed by radiation and chemotherapy. GBMs are highly heterogeneous, having a complex interaction among different cells within the tumor as well as the tumor microenvironment. One of the main challenges in the neuro-oncology field in general, and GBM in particular, is to find an optimum culture condition that maintains the molecular genotype and phenotype as well as heterogeneity of the original tumor in vitro and in vivo. Established cell lines were shown to be a poor model of the disease, failing to recapitulate the phenotype and harboring non-parental genotypic mutations. Given the growing understanding of GBM biology, the discovery of glioma cancer stem-like cells (GSCs), and their role in tumor formation and therapeutic resistance, scientists are turning more towards patient-derived cells and xenografts as a more representative model. In this review, we will discuss the current state of patient-derived GSCs and their xenografts; and provide an overview of different established models to study GBM biology and to identify novel therapeutics in the pre-clinical phase.

RARRES1 is a novel immune-related biomarker in GBM

Immunotherapy is a promising route for the treatment of glioblastoma (GBM). Researchers have conducted a large number of studies on the pathogenesis of GBM; however, these studies are not comprehensive. High-throughput sequence analysis allows for insights into the pathogenesis of GBM. In this study, we used The Cancer Genome Atlas dataset to identify the function of RARRES1 enriched in GBM, especially in the WHO grade-IV cases. We discovered that RARRES1 is highly expressed in patients with mesenchymal subtype, unmethylated MGMT, IDH1 wild type, and non-G-CIMP, all of which are molecular characteristics of malignant GBM. Results of the immune microenvironment analysis showed that RARRES1 is strongly correlated with dendritic cells PD1, PDL2, TIM3, and CTLA4, which are the immune checkpoints in GBM. Furthermore, according to the overall survival and status analysis, a high expression of RARRES1 was found to be an unfavorable factor for prognosis. This indicates that RARRES1 may participate in the pathogenesis and immune-related processes in GBM, and may serve as a therapeutic target.

Numerical Simulation of a Multiscale Cell Motility Model Based on the Kinetic Theory of Active Particles

In this work, we deal with a kinetic model of cell movement that takes into consideration the structure of the extracellular matrix, considering cell membrane reactions, haptotaxis, and chemotaxis, which plays a key role in a number of biological processes such as wound healing and tumor cell invasion. The modeling is performed at a microscopic scale, and then, a scaling limit is performed to derive the macroscopic model. We run some selected numerical experiments aimed at understanding cell movement and adhesion under certain documented situations, and we measure the alignment of the cells and compare it with the pathways determined by the extracellular matrix by introducing new alignment operators.

Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451–AMPK–mTOR–cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs.

Simulation analysis for tumor radiotherapy based on three-component mathematical models

OBJECTIVE

To setup a three-component tumor growth mathematical model and discuss its basic application in tumor fractional radiotherapy with computer simulation.

METHOD

First, our three-component tumor growth model extended from the classical Gompertz tumor model was formulated and applied to a fractional radiotherapy with a series of proper parameters. With the computer simulation of our model, the impact of some parameters such as fractional dose, amount of quiescent tumor cells, and α/β value to the effect of radiotherapy was also analyzed, respectively.

RESULTS

With several optimal technologies, the model could run stably and output a series of convergent results. The simulation results showed that the fractional radiotherapy dose could impact the effect of radiotherapy significantly, while the amount of quiescent tumor cells and α/β value did that to a certain extent.

CONCLUSIONS

Supported with some proper parameters, our model can simulate and analyze the tumor radiotherapy program as well as give some theoretical instruction to radiotherapy personalized optimization.

Synergistic Effects of Bortezomib-OV Therapy and Anti-Invasive Strategies in Glioblastoma: A Mathematical Model

It is well-known that the tumor microenvironment (TME) plays an important role in the regulation of tumor growth and the efficacy of anti-tumor therapies. Recent studies have demonstrated the potential of combination therapies, using oncolytic viruses (OVs) in conjunction with proteosome inhibitors for the treatment of glioblastoma, but the role of the TME in such therapies has not been studied. In this paper, we develop a mathematical model for combination therapies based on the proteosome inhibitor bortezomib and the oncolytic herpes simplex virus (oHSV), with the goal of understanding their roles in bortezomib-induced endoplasmic reticulum (ER) stress, and how the balance between apoptosis and necroptosis is affected by the treatment protocol. We show that the TME plays a significant role in anti-tumor efficacy in OV combination therapy, and illustrate the effect of different spatial patterns of OV injection. The results illustrate a possible phenotypic switch within tumor populations in a given microenvironment, and suggest new anti-invasion therapies.

Role of tumor-associated neutrophils in regulation of tumor growth in lung cancer development: A mathematical model

Neutrophils display rapid and potent innate immune responses in various diseases. Tumor-associated neutrophils (TANs) however either induce or overcome immunosuppressive functions of the tumor microenvironment through complex tumor-stroma crosstalk. We developed a mathematical model to address the question of how phenotypic alterations between tumor suppressive N1 TANS, and tumor promoting N2 TANs affect nonlinear tumor growth in a complex tumor microenvironment. The model provides a visual display of the complex behavior of populations of TANs and tumors in response to various TGF-β and IFN-β stimuli. In addition, the effect of anti-tumor drug administration is incorporated in the model in an effort to achieve optimal anti-tumor efficacy. The simulation results from the mathematical model were in good agreement with experimental data. We found that the N2-to-N1 ratio (N21R) index is positively correlated with aggressive tumor growth, suggesting that this may be a good prognostic factor. We also found that the antitumor efficacy increases when the relative ratio (Dap) of delayed apoptotic cell death of N1 and N2 TANs is either very small or relatively large, providing a basis for therapeutically targeting prometastatic N2 TANs.

Integrating in vitro experiments with in silico approaches for Glioblastoma invasion: the role of cell-to-cell adhesion heterogeneity

Glioblastoma cells adopt migration strategies to invade into the brain parenchyma ranging from individual to collective mechanisms, whose role and dynamics are not yet fully understood. In this work, we explore Glioblastoma heterogeneity and recapitulate its invasive patterns both in vitro, by utilizing primary cells along with the U87MG cell line, and in silico, by adopting discrete, individual cell-based mathematics. Glioblastoma cells are cultured three-dimensionally in an ECM-like substrate. The primary Glioblastoma spheroids adopt a novel cohesive pattern, mimicking perivascular invasion in the brain, while the U87MG adopt a typical, starburst invasive pattern under the same experimental setup. Mathematically, we focus on the role of the intrinsic heterogeneity with respect to cell-to-cell adhesion. Our proposed mathematical approach mimics the invasive morphologies observed in vitro and predicts the dynamics of tumour expansion. The role of the proliferation and migration is also explored showing that their effect on tumour morphology is different per cell type. The proposed model suggests that allowing cell-to-cell adhesive heterogeneity within the tumour population is sufficient for variable invasive morphologies to emerge which remain originally undetectable by conventional imaging, indicating that exploration in pathological samples is needed to improve our understanding and reveal potential patient-specific therapeutic targets.

Role of extracellular matrix and microenvironment in regulation of tumor growth and LAR-mediated invasion in glioblastoma

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical cues in the microenvironment. Recent studies have shown that miR-451 regulates downstream molecules including AMPK/CAB39/MARK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of the main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this complex process of cell proliferation and invasion and its response to conventional treatment, we propose a mathematical model that analyzes the intracellular dynamics of the miR-451-AMPK- mTOR-cell cycle signaling pathway within a cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress in response to fluctuating glucose levels. We show how up- or down-regulation of components in these pathways affects the key cellular decision to infiltrate or proliferate in a complex microenvironment in the absence and presence of time delays and stochastic noise. Glycosylated chondroitin sulfate proteoglycans (CSPGs), a major component of the extracellular matrix (ECM) in the brain, contribute to the physical structure of the local brain microenvironment but also induce or inhibit glioma invasion by regulating the dynamics of the CSPG receptor LAR as well as the spatiotemporal activation status of resident astrocytes and tumor-associated microglia. Using a multi-scale mathematical model, we investigate a CSPG-induced switch between invasive and non-invasive tumors through the coordination of ECM-cell adhesion and dynamic changes in stromal cells. We show that the CSPG-rich microenvironment is associated with non-invasive tumor lesions through LAR-CSGAG binding while the absence of glycosylated CSPGs induce the critical glioma invasion. We illustrate how high molecular weight CSPGs can regulate the exodus of local reactive astrocytes from the main tumor lesion, leading to encapsulation of non-invasive tumor and inhibition of tumor invasion. These different CSPG conditions also change the spatial profiles of ramified and activated microglia. The complex distribution of CSPGs in the tumor microenvironment can determine the nonlinear invasion behaviors of glioma cells, which suggests the need for careful therapeutic strategies.

Microglia/Astrocytes-Glioblastoma Crosstalk: Crucial Molecular Mechanisms and Microenvironmental Factors

In recent years, the functions of glial cells, namely, astrocytes and microglia, have gained prominence in several diseases of the central nervous system, especially in glioblastoma (GB), the most malignant primary brain tumor that leads to poor clinical outcomes. Studies showed that microglial cells or astrocytes play a critical role in promoting GB growth. Based on the recent findings, the complex network of the interaction between microglial/astrocytes cells and GB may constitute a potential therapeutic target to overcome tumor malignancy. In the present review, we summarize the most important mechanisms and functions of the molecular factors involved in the microglia or astrocytes-GB interactions, which is particularly the alterations that occur in the cell's extracellular matrix and the cytoskeleton. We overview the cytokines, chemokines, neurotrophic, morphogenic, metabolic factors, and non-coding RNAs actions crucial to these interactions. We have also discussed the most recent studies regarding the mechanisms of transportation and communication between microglial/astrocytes - GB cells, namely through the ABC transporters or by extracellular vesicles. Lastly, we highlight the therapeutic challenges and improvements regarding the crosstalk between these glial cells and GB.

Complex role of NK cells in regulation of oncolytic virus-bortezomib therapy

In the present work, we investigated the role of natural killer (NK) cells in combination therapy with oncolytic virus (OV) and bortezomib, a proteasome inhibitor. NK cells display rapid and potent immunity to metastatic and hematological cancers, and they overcome immunosuppressive effects of tumor microenvironment. We developed a mathematical model to address the question of how the density of NK cells affects the growth of the tumor. We found that the antitumor efficacy increases when the endogenous NKs are depleted and also when exogenous NK cells are injected into the tumor. These predictions were validated by our in vivo and in vitro experiments.

Sequential Therapeutic Response Modeling for Tumor Treatment Using Computational Hybrid Control Systems Approach

OBJECTIVE

Tumorigenesis is due to uncontrolled cell division arising from mutations and alterations in the proliferative controls of the cell population. The fight against tumor growth and development has often relied on combination therapy that has been acclaimed as one of the main standards of care in cancer therapeutics and prevention of drug-related resistances. The toxicity of the combinatorial drugs raises a significant concern whenever patients take two or more drugs concurrently at the maximum tolerated dose. A promising solution in tumor treatment involves the administration of the drugs in an alternating or sequential fashion rather than a simultaneous manner. In this paper, we investigate how feasible such an approach is from a mathematical perspective and propose a switched hybrid control systems framework.

METHODS

We explore the response of tumor cells dynamics to sequential drugs administration with the aid of a time-dependent switching strategy. A transit compartmentalized model is employed to describe the tumor cells progression to death.

RESULTS

The design of the time-based drug switching logic ensures the proliferating tumor cells are repressed.

CONCLUSIONS

Simulation results are provided using the tumor growth dynamics with sequential drugs intake to demonstrate the effectiveness of the proposed method in reducing the tumor size.

SIGNIFICANCE

This paper is the first attempt to provide a switched hybrid control systems framework on sequential drug administration to biomedical researchers and clinicians.

The role of myosin II in glioma invasion: A mathematical model

Gliomas are malignant tumors that are commonly observed in primary brain cancer. Glioma cells migrate through a dense network of normal cells in microenvironment and spread long distances within brain. In this paper we present a two-dimensional multiscale model in which a glioma cell is surrounded by normal cells and its migration is controlled by cell-mechanical components in the microenvironment via the regulation of myosin II in response to chemoattractants. Our simulation results show that the myosin II plays a key role in the deformation of the cell nucleus as the glioma cell passes through the narrow intercellular space smaller than its nuclear diameter. We also demonstrate that the coordination of biochemical and mechanical components within the cell enables a glioma cell to take the mode of amoeboid migration. This study sheds lights on the understanding of glioma infiltration through the narrow intercellular spaces and may provide a potential approach for the development of anti-invasion strategies via the injection of chemoattractants for localization.